Get Absolute Value(integer)

How to get absolute (integer) only use bit operators and +-*/.(In gcc version 4.4.3 (Ubuntu 4.4.3-4ubuntu5)  )

• if number >= 0 , then number >> 31 == 0

• if number < 0   , then number >> 31 == 0xFFFFFFFF

If some number exclusive or( xor ) 0xFFFFFFFF means each bit becomes its "opposite" number. (1 becomes 0, and 0 becomes 1).And If a number xor 0x00000000 means nothing happened to this number. So:

• number ^ 0xFFFFFFFF = ~number
• number ^ 0x00000000 = number

In this question, you should also know something about complement number(see two's complement). When a number is negative, |number| = ~number +1 or you can use |number| = !number + 1. When a number is positive, |number| = number.

If you know above, then the goal of |x| = (x^(x>>31))+(~(x>>31)+1).

(x^(x>>31)) means:

• x >= 0, x^(x>>31) = x^0x00000000 = x
• x < 0, x^(x>>31) = x^0xFFFFFFFF = ~x

And (~(x>>31)+1)means:

• x >= 0, ~(x>>31)+1 = 0xFFFFFFFF+1 = 0
• x < 0, ~(x>>31)+1 = 0x00000000+1 = 1

And we should take care of those brackets, because the priorities of operators are: ~ > */ > + - > bit operators(&,^,|)

Level	Operator	Description	Grouping
1	::	scope	Left-to-right
2	() [] . -> ++ -- dynamic_cast static_cast reinterpret_cast const_cast typeid	postfix	Left-to-right
3	++ -- ~ ! sizeof new delete	unary (prefix)	Right-to-left
	* &	indirection and reference (pointers)
	+ -	unary sign operator
4	(type)	type casting	Right-to-left
5	.* ->*	pointer-to-member	Left-to-right
6	* / %	multiplicative	Left-to-right
7	+ -	additive	Left-to-right
8	<< >>	shift	Left-to-right
9	< > <= >=	relational	Left-to-right
10	== !=	equality	Left-to-right
11	&	bitwise AND	Left-to-right
12	^	bitwise XOR	Left-to-right
13	|	bitwise OR	Left-to-right
14	&&	logical AND	Left-to-right
15	||	logical OR	Left-to-right
16	?:	conditional	Right-to-left
17	= *= /= %= += -= >>= <<= &= ^= |=	assignment	Right-to-left
18	,	comma	Left-to-right